{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2023 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# strimko2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/strimko2.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/strimko2.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "Strimko problem in Google CP Solver.\n",
    "\n",
    "  From\n",
    "  360: A New Twist on Latin Squares\n",
    "  http://threesixty360.wordpress.com/2009/08/04/a-new-twist-on-latin-squares/\n",
    "  '''\n",
    "  The idea is simple: each row and column of an nxn grid must contain\n",
    "  the number 1, 2, ... n exactly once (that is, the grid must form a\n",
    "  Latin square), and each \"stream\" (connected path in the grid) must\n",
    "  also contain the numbers 1, 2, ..., n exactly once.\n",
    "  '''\n",
    "\n",
    "  For more information, see:\n",
    "  * http://www.strimko.com/\n",
    "  * http://www.strimko.com/rules.htm\n",
    "  * http://www.strimko.com/about.htm\n",
    "  * http://www.puzzlersparadise.com/Strimko.htm\n",
    "\n",
    "  I have blogged about this (using MiniZinc model) in\n",
    "  'Strimko - Latin squares puzzle with \"streams\"'\n",
    "  http://www.hakank.org/constraint_programming_blog/2009/08/strimko_latin_squares_puzzle_w_1.html\n",
    "\n",
    "  Compare with the following models:\n",
    "  * MiniZinc: http://hakank.org/minizinc/strimko2.mzn\n",
    "  * ECLiPSe: http://hakank.org/eclipse/strimko2.ecl\n",
    "  * SICStus: http://hakank.org/sicstus/strimko2.pl\n",
    "  * Gecode: http://hakank.org/gecode/strimko2.cpp\n",
    "\n",
    "  This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
    "  See my other Google CP Solver models: http://www.hakank.org/google_or_tools/\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "from ortools.constraint_solver import pywrapcp\n",
    "\n",
    "\n",
    "def main(streams='', placed=''):\n",
    "\n",
    "  # Create the solver.\n",
    "  solver = pywrapcp.Solver('Strimko')\n",
    "\n",
    "  #\n",
    "  # default problem\n",
    "  #\n",
    "  if streams == '':\n",
    "    streams = [[1, 1, 2, 2, 2, 2, 2], [1, 1, 2, 3, 3, 3, 2],\n",
    "               [1, 4, 1, 3, 3, 5, 5], [4, 4, 3, 1, 3, 5, 5],\n",
    "               [4, 6, 6, 6, 7, 7, 5], [6, 4, 6, 4, 5, 5, 7],\n",
    "               [6, 6, 4, 7, 7, 7, 7]]\n",
    "\n",
    "    # Note: This is 1-based\n",
    "    placed = [[2, 1, 1], [2, 3, 7], [2, 5, 6], [2, 7, 4], [3, 2, 7], [3, 6, 1],\n",
    "              [4, 1, 4], [4, 7, 5], [5, 2, 2], [5, 6, 6]]\n",
    "\n",
    "  n = len(streams)\n",
    "  num_placed = len(placed)\n",
    "\n",
    "  print('n:', n)\n",
    "\n",
    "  #\n",
    "  # variables\n",
    "  #\n",
    "\n",
    "  x = {}\n",
    "  for i in range(n):\n",
    "    for j in range(n):\n",
    "      x[i, j] = solver.IntVar(1, n, 'x[%i,%i]' % (i, j))\n",
    "\n",
    "  x_flat = [x[i, j] for i in range(n) for j in range(n)]\n",
    "\n",
    "  #\n",
    "  # constraints\n",
    "  #\n",
    "\n",
    "  # all rows and columns must be unique, i.e. a Latin Square\n",
    "  for i in range(n):\n",
    "    row = [x[i, j] for j in range(n)]\n",
    "    solver.Add(solver.AllDifferent(row))\n",
    "\n",
    "    col = [x[j, i] for j in range(n)]\n",
    "    solver.Add(solver.AllDifferent(col))\n",
    "\n",
    "  #\n",
    "  # streams\n",
    "  #\n",
    "  for s in range(1, n + 1):\n",
    "    tmp = [x[i, j] for i in range(n) for j in range(n) if streams[i][j] == s]\n",
    "    solver.Add(solver.AllDifferent(tmp))\n",
    "\n",
    "  #\n",
    "  # placed\n",
    "  #\n",
    "  for i in range(num_placed):\n",
    "    # note: also adjust to 0-based\n",
    "    solver.Add(x[placed[i][0] - 1, placed[i][1] - 1] == placed[i][2])\n",
    "\n",
    "  #\n",
    "  # search and solution\n",
    "  #\n",
    "  db = solver.Phase(x_flat, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)\n",
    "\n",
    "  solver.NewSearch(db)\n",
    "\n",
    "  num_solutions = 0\n",
    "  while solver.NextSolution():\n",
    "    for i in range(n):\n",
    "      for j in range(n):\n",
    "        print(x[i, j].Value(), end=' ')\n",
    "      print()\n",
    "\n",
    "    print()\n",
    "    num_solutions += 1\n",
    "\n",
    "  solver.EndSearch()\n",
    "\n",
    "  print()\n",
    "  print('num_solutions:', num_solutions)\n",
    "  print('failures:', solver.Failures())\n",
    "  print('branches:', solver.Branches())\n",
    "  print('WallTime:', solver.WallTime(), 'ms')\n",
    "\n",
    "\n",
    "if len(sys.argv) > 1:\n",
    "  problem_file = sys.argv[1]\n",
    "  exec(compile(open(problem_file).read(), problem_file, 'exec'))\n",
    "  main(streams, placed)\n",
    "else:\n",
    "  main()\n",
    "\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 5
}
